Related Works:
The use of ML for solving PDEs has gained tremendous traction in the past few years. Much of the research has focused on improving neural network architectures and optimization techniques to enable generalizable and accurate learning of PDE solutions. More recently, there has been a lot of focus on learning PDE operators with neural networks (NNs) [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. The neural operators are trained on high-fidelity solutions generated by traditional PDE solvers on a computational grid of specific resolution and do not require any knowledge of the PDE. However, accuracy and out-of-distribution generalizability deteriorates as the resolution of computational grid increases (for example, \(2048^2\)  in 2-D or \(256^3\)  in 3-D). Furthermore, these methods are limited by an upper cap on GPU memory.
